Bulk viscosity of strongly coupled plasmas with holographic duals

TL;DR

The paper develops a holographic method to compute the bulk viscosity $\zeta$ of strongly coupled plasmas with a single-scalar gravity dual by leveraging a Kubo formula and the low-frequency limit of a mixed graviton-scalar Green's function. By solving a reduced bulk perturbation equation and evaluating a conserved horizon flux, it yields a practical route to extract $\zeta$ alongside the shear viscosity $\eta$, with analytic results in Chamblin-Reall backgrounds and numerical results for QCD-like potentials. The study finds that $\zeta/\eta$ can approach, and in some cases slightly violate, Buchel's proposed bound, depending on the equation of state encoded by the scalar potential. These findings enhance understanding of non-conformal transport in holographic plasmas and provide a computationally efficient framework for studying bulk viscosity in AdS/CFT models relevant to QCD phenomenology.

Abstract

We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in arXiv:0708.3459.

Figures (3)

• Figure 1: A cartoon of the relation between shear viscosity and $h_{12}$ graviton absorption, and between bulk viscosity and absorption of a mixture of the $h_{ii}$ graviton and the scalar $\phi$.
• Figure 2: $s/T^3$ as a function of $T/T_c$ for two potentials of the form \ref{['QCDLikePotential']} with $\{\gamma\approx 0.606,b\approx 2.06,\Delta\approx 3.93\}$ and $\{\gamma\approx 0.606,b \approx 1.503,\Delta \approx 3.61\}$. For each curve, $T_c$ is defined to be the ordinate of its inflection point. These potentials were obtained in Gubser:2008nyGubser:2008yx where their equations of state are shown to mimic that of QCD.
• Figure 3: The ratio $\zeta/s$ (dotted) for two potentials of the form \ref{['QCDLikePotential']}, whose equations of state were plotted in figure \ref{['fig:QCDLikePotentialEOS']}. The solid curves show the Buchel bound \ref{['BuchelBound']}, and a violation is evident when $T$ is below $T_c$ for both potentials.